Dissection of square to two identical polygons

Author : Gavin Theobald

2×{3} Triangle
2×{4} Square
2×{5} Pentagon
2×{6} Hexagon
2×{7} Heptagon
2×{8} Octagon
2×{9} Enneagon
2×{10} Decagon
2×{11} Hendecagon
2×{12} Dodecagon
2×{5/2} Pentagram
2×{6/2} Hexagram
2×{8/2} Octagram
2×{8/3} Octagram
2×{10/4} Decagram
2×{12/2}  Dodecagram
2×{12/3}  Dodecagram
2×{R√2} Silver Rectangle
2×{Rϕ} Golden Rectangle
2×{R2} Domino
2×{G} Greek Cross
2×{L} Latin Cross
2×{Gc} Curved Greek Cross
2×{Lc} Curved Latin Cross
2×{M} Maltese Cross
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5 4 8 7 11 10 13 10 14 8


5/2 6/2 7/2 7/3 8/2 8/3 9/2 9/3 9/4 10/2 10/3 10/4 12/2 12/3 12/4 12/5
12 9 1110 10 16 1514 14

2 x Triangle

Square — 2 × Triangle (5 pieces)

Discovered by Ernest Irving Freese.

The dissection is translational.
2 x Square

Square — 2 × Square (4 pieces)

The dissection is translational and hingeable.
2 x Pentagon

Square — 2 × Pentagon (8 pieces)

 2 x Hexagon

Square — 2 × Hexagon (7 pieces)

The dissection is translational.
2 x Heptagon

Square — 2 × Heptagon (11 pieces)

 2 x Octagon

Square — 2 × Octagon (10 pieces)

 2 x Enneagon

Square — 2 × Enneagon (13 pieces)

 2 x Decagon

Square — 2 × Decagon (10 pieces)

 2 x Hendecagon

Square — 2 × Hendecagon (14 pieces)

 2 x Dodecagon

Square — 2 × Dodecagon (8 pieces)

Discovered by Ernest Irving Freese.
2 x Pentagram

Square — 2 × Pentagram (12 pieces)

 2 x Hexagram

Square — 2 × Hexagram (9 pieces)

The dissection is translational.
2 x Octagram

Square — 2 × Octagram {8/2} (11 pieces)

2 x Octagram

Square — 2 × Octagram {8/2} (10 pieces with 3 turned over)

I discovered the original dissection, but Greg Frederickson worked out how to save a piece by turning over pieces.
2 x Octagram

Square — 2 × Octagram {8/3} (10 pieces)

 2 x Decagram

Square — 2 × Decagram {10/4} (16 pieces)

 2 x Dodecagram

Square — 2 × Dodecagram {12/2} (15 pieces)

2 x Dodecagram

Square — 2 × Dodecagram {12/2} (14 pieces with 1 turned over)

 2 x Dodecagram

Square — 2 × Dodecagram {12/3} (14 pieces)

 2 x Silver Rectangle

Square — 2 × Silver Rectangle (5 pieces)

The dissection is translational.
2 x Golden Rectangle

Square — 2 × Golden Rectangle (5 pieces)

The dissection is translational.
2 x Domino

Square — 2 × Domino (2 pieces)

The dissection is translational.
2 x Greek Cross

Square — 2 × Greek Cross (4 pieces)

Discovered by Sam Loyd (1893).

The dissection is translational and hingeable.
2 x Latin Cross

Square — 2 × Latin Cross (7 pieces)

 2 x Curved Greek Cross

Square — 2 × Curved Greek Cross (13 pieces)

 2 x Curved Latin Cross

Square — 2 × Curved Latin Cross (16 pieces)

 2 x Maltese Cross

Square — 2 × Maltese Cross (12 pieces)

The dissection is translational and hingeable.